Divide the following complex numbers: $\dfrac{12 e^{3\pi i / 4}}{2 e^{\pi i / 12}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Answer: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $12 e^{3\pi i / 4}$ ) has angle $\frac{3}{4}\pi$ and radius 12. The second number ( $2 e^{\pi i / 12}$ ) has angle $\frac{1}{12}\pi$ and radius 2. The radius of the result will be $\frac{12}{2}$ , which is 6. The angle of the result is $\frac{3}{4}\pi - \frac{1}{12}\pi = \frac{2}{3}\pi$ The radius of the result is $6$ and the angle of the result is $\frac{2}{3}\pi$.